If I might. Op, here's the thing.
You're dealing with faggots.
The thing you want to avoid, MOST OF ALL, is any impression that you might be out to harsh their mary sue buzz. Don't talk weapons unless THEY start pulling shit first, or you might start to look like a bad guy. In their beady little mary sue eyes, you're conspicuously NOT a mary sue, and are therefore automatically suspect.
Instead, here's what you do. You position yourself as a geek with a hardon for space colonization. The kind of fag who tears up at rocket launches. It helps if you are that kind of fag (as I am), but even if not, it's a believable OOC cover story.
Ask your dm, when you send a colony ship to an uninhabited planet, how long before that planet can send colony ships of its own. If the DM wants to handle colonization, it'll be a sizable time period, but not a crazy one. You're a robot, you don't need to worry about people growing up. Your production is your production.
Then, start pumping out colony ships as fast as you can. Three planets, three new planets per turn. Eventually, your new planets per turn will itself start growing by three per turn. Then you've won.
All the while, put a god damn smile on your face and never take it off. Be friendly, and engaging. Humor their furfaggotry shit. If at least one of your colonies is up and running and the mary sue wants to blow up your home planet, probably as some kind of ego trip, smile sadly and let them. But mark that player.
He will be the first to die.
It really doesn't matter what tech you use. With a 5 trillion world playing field, if you colonize faster and farther than they can, you can use fucking blowguns and rose petals and still overwhelm their armies. It's a good thing they're all mary sues, because they're going to need all the bullshit "my psychic powers BLOW UP half your battleships!" cards they can find.
And the best thing? It will have been a fair fight.